I want to calculate area weighted average of districts of India.
I have Particulate matter 2.5(PM2.5) data for Districts of India, and now I want to find area weighted average of PM2.5 for each of these districts.
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You could use the approach of creating spatial weight index it is defined as:
A spatial weights matrix is a representation of the spatial structure of your data. It is a quantification of the spatial relationships that exist among the features in your dataset (or, at least, a quantification of the way you conceptualize those relationships). Because the spatial weights matrix imposes a structure on your data, you should select a conceptualization that best reflects how features actually interact with each other (giving thought, of course, to what it is you are trying to measure). If you are measuring clustering of a particular species of seed-propagating tree in a forest, for example, some form of inverse distance is probably most appropriate. However, if you are assessing the geographic distribution of a region's commuters, travel time or travel cost might be a better choice.
Spatial relationships based on polygon contiguity, Queen's case: shared edges or nodes
I also came across another approach from a different thread posted, Calculating area weighted average of attribute in one layer by shape in another using ArcGIS for Desktop?
That might also shed some light on an approach to help you.